Filter for a modulator and methods thereof

ABSTRACT

In some exemplary embodiments of the invention, a transfer function of a filter for a fractional-N sigma-delta modulator may be calculated to be optimized according to predefined optimization criteria. For example, the optimization criteria may include spectral cleanliness at the output of the modulator, or the mean squared error of the input to the filter and the input to a voltage controlled oscillator of the fractional-N phase locked loop (PLL). In some exemplary embodiments, the filter may be adjusted to compensate for variations and/or impairments in the analog fractional-N PLL. A non-exhaustive list of examples for the transfer function includes a finite impulse response and an infinite impulse response.

BACKGROUND OF THE INVENTION

In polar modulation, a signal is separated into its instantaneousamplitude and phase/frequency components (rather than into the classicalin-phase (I) and quadrature (Q) components), and the amplitude componentand phase/frequency component are modulated independently. The amplitudecomponent may be modulated with any suitable amplitude modulation (AM)technique, while the phase/frequency component may be modulated using ananalog phase locked loop (PLL).

To allow reasonable operation, the bandwidth of the PLL may be quitesmall, much smaller than the actual bandwidth of the transmissionsignal's instantaneous phase/frequency. For example, in the case wherethe PLL is fed by a sigma-delta converter that has a high pass noisenature, the loop filter may be narrow enough to attenuate thesigma-delta quantization noise and the phase noise of the PLL. Apre-emphasis filter may emphasize, prior to modulation, those frequencycomponents that would be attenuated by the PLL. The pre-emphasis filtermay employ inverse filtering to the linearized response of the PLL. Thisinverse filtering may yield a high-order infinite impulse response(IIR), which may suffer from stability problems.

Conventional practice involves calibration mechanisms in order toaccurately calibrate the PLL to the predefined pre-emphasis filter.Without calibration, there is a risk that the pre-emphasis filter willnot match the inverse to the PLL closed loop transfer function, whichmay result in enhancement of the phase noise.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention are illustrated by way of example and notlimitation in the figures of the accompanying drawings, in which likereference numerals indicate corresponding, analogous or similarelements, and in which:

FIG. 1 is a block-diagram illustration of an exemplary communicationsystem including a transmitter according to some embodiments of theinvention;

FIG. 2 is a block-diagram illustration of an exemplary fractional-Nsigma-delta modulator according to some embodiments of the invention;

FIG. 3 is a flowchart illustration of an exemplary method to determine atransfer function of a filter, according to some embodiments of theinvention;

FIG. 4 is a block-diagram illustration of an exemplary fractional-Nsigma-delta modulator including an adaptive filter, according to someembodiments of the invention;

FIG. 5 is a block-diagram illustration of an exemplary linearizedapproximation to the exemplary fractional-N sigma-delta modulator ofFIG. 2, according to some embodiments of the invention;

FIG. 6 is a block diagram of an exemplary system including an equalizer.

It will be appreciated that for simplicity and clarity of illustration,elements shown in the figures have not necessarily been drawn to scale.For example, the dimensions of some of the elements may be exaggeratedrelative to other elements for clarity.

DETAILED DESCRIPTION OF THE INVENTION

In the following detailed description, numerous specific details are setforth in order to provide a thorough understanding of embodiments of theinvention. However it will be understood by those of ordinary skill inthe art that embodiments of the invention may be practiced without thesespecific details. In other instances, well-known methods, procedures,components and circuits have not been described in detail so as not toobscure the description of embodiments of the invention.

FIG. 1 is a block-diagram illustration of an exemplary communicationsystem including a transmitter according to an embodiment of theinvention. A communication device 100 is able to communicate with acommunication device 102 over a communication channel 104. Although thescope of the invention is not limited in this respect, the communicationsystem shown in FIG. 1 may be part of a cellular communication system(with one of communication devices 100, 102 being a base station and theother a mobile station, or with both communication devices 100, 102being mobile stations), a pager communication system, a personal digitalassistant and a server, etc. A non-exhaustive list of examples for thecommunication system shown in FIG. 1 includes a Global System for MobileCommunications (GSM) system, a General Packet Radio Service (GPRS)system, an Enhanced Data for GSM Evolution (EDGE) system, code divisionmultiple access (CDMA), CDMA2000, Wideband-CDMA (WCDMA), AMPS and anyother wireless standard.

Communication device 100 may include at least a transmitter 106 and anantenna 108. Communication device 102 may include at least a receiver110 and an antenna 112. Antennas 108 and 112 may be of any desired kindsuch as, but not limited to, dipole, Yagi and multi-pole and the like.Moreover, communication device 100 may include a receiver (not shown).Similarly, communication device 102 may include a transmitter (notshown).

Transmitter 106 may include at least a baseband symbol generator 114 togenerate a signal of baseband symbols, a splitter 116 to split thesignal into its instantaneous amplitude and phase/frequency components,an amplitude path 118 to modulate and amplify the amplitude components,a fractional-N sigma-delta modulator 120 to modulate and up-convert thephase/frequency components, and a power amplifier 122 to amplify theoutput of fractional-N sigma-delta modulator 120 with a gain controlledby the output of amplitude path 118. Antenna 108 is coupled to poweramplifier 122 to transmit the output of power amplifier 122.

Baseband symbol generator 114 may be implemented in accordance with awireless standard. Splitter 116 may be implemented in hardware, softwareor firmware or any combination thereof.

FIG. 2 is a block-diagram illustration of an exemplary fractional-Nsigma-delta modulator according to an embodiment of the invention, suchas, for example, fractional-N sigma-delta modulator 120 of FIG. 1.Fractional-N sigma-delta modulator 120 has a digital portion and ananalog portion. The digital portion may include at least adifferentiator 202, a filter 204 (such as, for example, a pre-emphasisfilter), an amplifier 206, a summer 208, and a sigma-delta converter210. The analog portion, which implements an analog phase locked loop(PLL) 212, may include at least a non-linear frequency divider 214, areference oscillator 216 to produce a signal having a frequency F_(REF),a non-linear phase-frequency detector 218, a loop filter 220, anamplifier 222 having a gain K_(V), and a voltage-controlled oscillator(VCO) 224. The input of VCO 224 is denoted Y. PLL 212 is also known as a“fractional-N phase locked loop” unit. Amplifier 222 and VCO 224 may beimplemented as a single unit (VCO 223); the separation into two elementsis for the sake of analysis.

Reference oscillator 216 may produce a signal having a referencefrequency F_(REF). An example of reference frequency F_(REF) isapproximately 26 MHz, although other reference frequencies may be usedinstead.

Differentiator 202 may differentiate the phase symbols received fromsplitter 116 of FIG. 1 to obtain the instantaneous frequency W of thebaseband signal. Differentiator 202 may be implemented in hardware,software or firmware or any combination thereof.

Filter 204 may be determined so that the instantaneous frequency W istransferred to the input Y of VCO 224 with little or no distortion, aswill be described in more detail hereinbelow. Any implementation of adigital filter is suitable for filter 204.

Amplifier 206 may normalize the output of filter 204, denoted X, to PLLreference frequency units.

Summer 208 may add the output of amplifier 206 with a number N+β. Boththe integer number N and the non-integer number β having a value between0 and 1 may be set according to an instruction from a base stationregarding the average output frequency of a transmitter of a mobilestation. For example, if reference frequency F_(REF) is approximately 26MHz, then N may have a value in the range of 29-32 so that N·F_(REF) hasa value of approximately 800 MHz.

Sigma-delta converter 210 may convert the output of summer 208 into aninteger number that represents the instantaneous frequency divisionratio of the PLL.

Non-linear frequency divider 214 may divide the output of VCO 224 by theinteger number provided by sigma-delta converter 210 to produce adivided-frequency signal.

Non-linear phase-frequency detector 218 may compare thedivided-frequency signal to the reference frequency signal produced byreference oscillator 216. Non-linear phase-frequency detector 218 mayproduce a control signal that corresponds to the phase difference and/orfrequency difference between the two signals. Any implementation of aphase-frequency detector is suitable for phase-frequency detector 218.

The control signal, after smoothing by loop filter 220 and amplificationby amplifier 222, may be applied to VCO 224 so that VCO 224 synthesizesa modulated output carrier signal.

As mentioned above, filter 204 may be determined so that theinstantaneous frequency W is transferred to the input Y of VCO 224 withlittle or no distortion (e.g. the overall response from W to Y is closeto flat in the frequencies of interest).

FIG. 3 is a flowchart illustration of an exemplary method to determine atransfer function C of filter 204, according to an embodiment of theinvention. The method may include the following:

-   a) building a linear model for PLL 212 and calculating the transfer    function H(w) from the output X of filter 204 to the input Y to VCO    224 (block 302);-   b) optionally adding various impairments of the different PLL    components (e.g. phase noises, variations of the PLL parameters from    their nominal values, and the like) to the model (block 304)—the    variations of PLL parameters from their nominal values, such as, for    example, capacitors, resistors, open loop gain, etc., may be due to    production inaccuracies;-   c) deciding on a topology for the transfer function C of filter 204    (block 306), and-   d) calculating a transfer function C to minimize a predefined cost    function related to the instantaneous frequency Wand the input Y to    VCO 224 (block 308).

In some embodiments, the transfer function C is a stable transferfunction.

Mathematically, the transfer function C may be expressed as follows:C=ArgMin_(C){Cost(W, Y)}.

In one embodiment, the cost function may be the mean square error (MSE)between the instantaneous frequency W and the input Y to VCO 224, asfollows: Cost(W,Y)=E{|W(t)−Y(t)|²}, where t is a time variable and E isan expectation operator. In yet another embodiment, the expectationoperator is replaced by time averaging and the cost function becomes:${{Cost}\quad\left( {W,Y} \right)} = {\frac{1}{T}{\int\limits_{{- T}/2}^{T/2}{{{{W(t)} - {Y(t)}}}^{2}{\mathbb{d}t}}}}$where T is a design parameter determining the integration time window.

In another embodiment, the cost function may be a weighted MSE in thefrequency domain, as follows:${{{Cost}\quad\left( {W,Y} \right)} = {E\left\{ {\int\limits_{- \infty}^{+ \infty}{{P(w)}{{{W(w)} - {Y(w)}}}^{2}{\mathbb{d}w}}} \right\}}},$where P(w) is a user-defined, positive, weight function. For example,weight function P(w) may give more weight to those frequencies wherespectral cleanliness is more important.

In other embodiments, other cost functions may be used, such as, forexample, a cost function that measures the spectral cleanliness of theoverall transmission signal.

In the event that an MSE or weighted MSE cost function is used, thenblock 304 of the method may be redundant if all impairments may berepresented as additive noise terms, since different choices of transferfunction C will not affect that total contribution of these additiveimpairments to the MSE or weighted MSE cost.

Certain cost functions may be minimized using equalization theory, aswill be described hereinbelow for a particular example.

Any suitable topology for transfer function C may be used in block 306.For example, transfer function C may be a finite impulse response (FIR)of order p (in which case stability is guaranteed), or an infiniteimpulse response (IIR) having a rational transfer function of orders(p,q), etc.

FIG. 4 is a block diagram of an exemplary fractional-N sigma-deltamodulator 420 including an adaptive filter, according to someembodiments of the invention. Fractional-N sigma-delta modulator 420 issimilar to fractional-N sigma-delta modulator 120 of FIG. 2, andtherefore similar components are referenced with the same referencenumerals and will not be described in further detail. Fractional-Nsigma-delta modulator 420 may include at least an adaptive filter 404(such as, for example, an adaptive pre-emphasis filter). Adaptive filter404 may include at least filter 204, an analog-to-digital (A/D)converter 402 and an adaptive algorithm 403.

Adaptive algorithm 403 compares the input to filter 204 (theinstantaneous frequency W) to the input to VCO 223 (after digitization).Adaptive algorithm 403 adapts filter 204 according to the comparison.For example, if the error between instantaneous frequency W and input Yis defined by a particular cost function, then adaptive algorithm 403may reduce the error iteratively. A non-exhaustive list of examples ofadaptive mechanisms include Least Mean Squares (LMS), Recursive LeastSquares (RLS), and the like. Thus, any impairments, offsets, drifts,etc. of the analog portion of the PLL may drive the filter values tothose values that minimize a pre-specified adaptive mechanism costfunction such as, for example, a mean squared error cost function.Variations in the PLL, such as for example, variations in temperature,voltage, aging, etc., may be compensated for by the adaptive algorithm.

Since adaptive algorithm 403 enables the digital values of filter 204 tobe adapted to variations in the analog PLL, it may not be necessary tocalibrate PLL 212 to predefined values for filter 204.

Block 302 of the method of FIG. 3 includes building a linear model of aPLL. FIG. 5 is a block diagram of an exemplary linearized approximationto the exemplary fractional-N sigma-delta modulator of FIG. 2. In thisapproximation, which is made in the phase domain, PLL 212 has beenapproximated by a linearized PLL 512, and sigma-delta converter 210 hasbeen approximated by a linearized sigma-delta converter 510 including anall pass filter and an additive noise n(Σ−Δ).

Non-linear frequency divider 214 has been approximated by a linearizedfrequency divider 514 including an amplifier 511 having a gain of2πF_(REF), a differentiator block 530 having a transfer function of s,where s is a Laplace domain variable, a subtraction block 532, anamplifier 534 having a gain of 1/(N+β), and an integrator block 536having a transfer function of 1/s.

VCO 224 has been approximated by a block 524 having a transfer functionof 1/s. Non-linear phase-frequency detector 218 has been approximated bya subtraction block 518, and loop filter 220 has been approximated by ablock 520 having a transfer function T(s).

The transfer function from the output X of filter 204 to input Y toblock 524 is then given by the following expression: $\begin{matrix}{\frac{Y(s)}{X(s)} = \frac{\left( {K_{V}/\left( {N + \beta} \right)} \right) \cdot {{T(s)}/s}}{1 + {\left( {K_{V}/\left( {N + \beta} \right)} \right) \cdot {{T(s)}/s}}}} & \left( {{Equation}\quad 1} \right)\end{matrix}$

The design of the transfer function C of filter 204 may then beperformed as follows. In order that the instantaneous frequency W betransferred to the input Y of VCO 224 with little or no frequency andphase distortion, the overall transfer function from W to Y may be ofsubstantially 0 dB gain up to a cut-off frequency f₀ and may havesubstantially linear phase up to the cut-off frequency f₀.

The cut-off frequency f₀ may be defined experimentally by observing thespectrum of the instantaneous frequency W signal. Alternatively, thecut-off frequency f₀ may be defined as narrow as possible while stillmeeting the requirements of a communication standard. Other definitionsof the cut-off frequency f₀ are also within the scope of the invention.

One straightforward solution is to define the transfer function C from Wto X up to the cut-off frequency f₀ as the inverse IIR to the transferfunction Y(s)/X(s), as given by the following expression:$\begin{matrix}\begin{matrix}{{\frac{X(s)}{W(s)} = \frac{1 + {\left( {K_{V}/\left( {N + \beta} \right)} \right) \cdot {{T(s)}/s}}}{\left( {K_{V}/\left( {N + \beta} \right)} \right) \cdot {{T(s)}/s}}},} \\{{{s = {{j \cdot 2}\pi\quad f}},{f < f_{0}}}\quad}\end{matrix} & \left( {{Equation}\quad 2} \right)\end{matrix}$where j is the square root of −1.

However, if the transfer function C were implemented as the inverse IIRto the transfer function Y(s)/X(s), then the following problems mightarise:

-   -   a) zeros and poles may need to be added to the inverse IIR to        stabilize the filter;    -   b) additional poles or filters may need to be added to the        inverse IIR to attenuate the frequencies above the cut-off        frequency f₀ so that the sigma-delta converter will not be        forced into saturation and so as not to increase the        quantization noise; and    -   c) the order of the transfer function C would no longer be a        design parameter; rather, it would have a one-to-one relation to        the order of the closed loop transfer function. Therefore,        according to some embodiments of the present invention, the        transfer function C is not the inverse IIR to the transfer        function Y(s)/X(s). Rather, the transfer function C of the        filter is calculated to optimize predefined optimization        criteria, as described hereinabove with respect to FIG. 3.

Block 302 of the method of FIG. 3 includes calculating the transferfunction C to minimize a predefined cost function related to theinstantaneous frequency W and the input Y to the VCO of the PLL. Thetransfer function C may be calculated in a manner similar to thecalculation of a minimum mean squared error (MMSE) equalizer, as will beexplained in greater detail. FIG. 6 is a block diagram of an exemplarysystem including an equalizer.

A known digital input signal u(i) may be subjected to an impulseresponse h, where the impulse response h is defined as the bi-lineartransform of the transfer function Y(s)/X(s).

An additive white Gaussian noise n_AWGN(i) may be shaped by a shapingfilter g. Noise shaping filter g may be a high pass filter with acut-off above frequency f₀, so that the equalizer response at highfrequencies will be attenuated.

The combination of shaped noise n(i) and the output of impulse responseh is denoted v(i). The digital signal v(i) may be subjected to a FIRfilter C to yield a digital signal u(i).

FIR filter C may be calculated analytically to minimize the mean squareerror that is defined ase≡u(i)−{circumflex over (u)}(i).  (Equation 3)

The following expressions may be useful in the calculation of FIR filterC:{circumflex over (u)}(i)={overscore (C)} ^(H) ·{overscore(V)},  (Equation 4a){overscore (V)}=H·{overscore (U)}+{overscore (N)},  (Equation 4b)$\begin{matrix}{{H \equiv \begin{bmatrix}{h\left( {M + L} \right)} & \cdots & {h(L)} & \cdots & {h\left( {{- M} + L} \right)} \\\vdots & \quad & \vdots & \quad & \vdots \\{h(M)} & \quad & {h(0)} & \quad & {h\left( {- M} \right)} \\\vdots & \quad & \vdots & \quad & \vdots \\{h\left( {M - L} \right)} & \cdots & {h\left( {- L} \right)} & \cdots & {h\left( {{- M} - L} \right)}\end{bmatrix}_{\lbrack{{({{2L} + 1})} \times {({{2M} + 1})}}\rbrack}},} & \left( {{Equation}\quad 4c} \right) \\{{\overset{\_}{U} \equiv \begin{bmatrix}{u\left( {i - M} \right)} \\\vdots \\{u(i)} \\\quad \\{u\left( {i + M} \right)}\end{bmatrix}_{\lbrack{{({{2M} + 1})} \times 1}\rbrack}},} & \left( {{Equation}\quad 4d} \right) \\{{\overset{\_}{N} \equiv \begin{bmatrix}{n\left( {i + L} \right)} \\\vdots \\{n(i)} \\\quad \\{u\left( {i - L} \right)}\end{bmatrix}_{\lbrack{{({{2L} + 1})} \times 1}\rbrack}},} & \left( {{Equation}\quad 4e} \right)\end{matrix}$where the bar denotes vector notation, the superscript H denotes theconjugate transpose, 2M+1 is assumed to be the length (i.e. number ofcoefficients) of impulse response h, and 2L+1 is assumed to be thelength (i.e. number of coefficients) of the equalizer.

The following assumptions may be made:

-   1. There is no correlation between the error and the observations.    Thus, E{e(i)·{overscore (V)}^(H)}={overscore (0)}^(H), where, again,    E is an expectation operator.-   2. There is no correlation between the input signal and the shaped    noise. Thus E{e(i)·n(i+k)^(*)}=0, ∀k, where the asterisk denotes the    complex conjugate.-   3. The input signal is independently distributed (ID). Thus    ${E\left\{ {{u(i)} \cdot {u\left( {i + k} \right)}^{*}} \right\}} = \left\{ {\begin{matrix}    {{\sigma_{U}^{2}(i)},{k = 0}} \\    {{0,{k \neq 0}}\quad}    \end{matrix},{{{where}\quad{\sigma_{U}^{2}(i)}} = {E{\left\{ {\cdot {{u(i)}}^{2}} \right\}.}}}} \right.$-   4. n_AWGN is additive white Gaussian noise. Thus    ${E\left\{ {{n\_ AWGN}{(i) \cdot {n\_ AWGN}}\left( {i + k} \right)^{*}} \right\}} = \left\{ {\begin{matrix}    {\sigma_{N\_ AWGN}^{2},{k = 0}} \\    {{0,{k \neq 0}}\quad}    \end{matrix},} \right.$    where σ_(N) _(—AWGN) ²=E{·|n₁₃ AWGN(i)|²} is a fixed value for all    i.

From assumption 1 it follows thatE{u(i)·{overscore (V)} ^(H) }=E{û(i)·{overscore (V)} ^(H)}.  (Equation5)

By substituting Equations 4a, 4b, 4d and 4e into Equation 5, it followsthat: $\begin{matrix}\begin{matrix}{{E\left\{ {{\hat{u}(i)} \cdot {\overset{\_}{V}}^{H}} \right\}} = {{{\overset{\_}{C}}^{H} \cdot E}\left\{ {\overset{\_}{V} \cdot {\overset{\_}{V}}^{H}} \right\}}} \\{= {{{\overset{\_}{C}}^{H} \cdot E}\left\{ {\left( {{H \cdot \overset{\_}{U}} + \overset{\_}{N}} \right) \cdot \left( {{{\overset{\_}{U}}^{H} \cdot H^{H}} + {\overset{\_}{N}}^{H}} \right)} \right\}}} \\{{= {{\overset{\_}{C}}^{H} \cdot \left\lbrack {{E\left\{ {H \cdot \overset{\_}{U} \cdot {\overset{\_}{U}}^{H} \cdot H^{H}} \right\}} + {E\left\{ {\overset{\_}{N} \cdot {\overset{\_}{N}}^{H}} \right\}}} \right\rbrack}},} \\{= {{\overset{\_}{C}}^{H} \cdot \left\lbrack {{H \cdot H^{H} \cdot \sigma_{U}^{2}} + {G \cdot G^{H} \cdot \sigma_{N\_ AWGN}^{2}}} \right\rbrack}}\end{matrix} & \left( {{Equation}\quad 6} \right)\end{matrix}$where for simplicity, σ_(U) ²(i) is denoted by σ_(U) ², and where matrixG is defined in terms of shaping filter g in a similar manner to thedefinition of matrix H in terms of impulse response h.

Similarly, using Equation 4b and assumptions 2 and 3, it follows that:$\begin{matrix}{\begin{matrix}{{E\left\{ {{u(i)} \cdot {\overset{\_}{V}}^{H}} \right\}} = {E\left\{ {{u(i)} \cdot \left( {{H \cdot \overset{\_}{U}} + \overset{\_}{N}} \right)} \right\}}} \\{= {\sigma_{U}^{2} \cdot \left\lbrack {{h(L)}\quad\ldots\quad{h(0)}\quad\ldots\quad{h\left( {- L} \right)}} \right\rbrack}}\end{matrix}.} & \left( {{Equation}\quad 7} \right)\end{matrix}$

From Equations 5, 6 and 7, and applying the complex conjugate operator,the MMSE analytical calculation of the FIR filter C is as follows:$\begin{matrix}{C = {\left\lbrack {{H \cdot H^{H} \cdot \sigma_{U}^{2}} + {G \cdot G^{H} \cdot \sigma_{N\_ AWGN}^{2}}} \right\rbrack^{- 1} \cdot \begin{bmatrix}{h(L)} \\\vdots \\{h(0)} \\\vdots \\{h\left( {- L} \right)}\end{bmatrix} \cdot {\sigma_{U}^{2}.}}} & \left( {{Equation}\quad 8} \right)\end{matrix}$

FIR filter C may be calculated empirically. For example, a simulationenvironment may be built in which u(i) is the instantaneous frequency atthe baseband, h(i) is the total response from the input to thesigma-delta converter until the input to the VCO, shaping filter g(i) ischosen so that shaped noise n(i) will be a high pass noise a cutofffrequency of which is beyond the band of interest of the total response.A simulation may then be run to determine empirical values for v(i). Thefollowing quantities may then be calculated: $\begin{matrix}{{R_{VV} = {\frac{1}{L} \cdot {\sum\limits_{k = 0}^{L - 1}{{\overset{\_}{V}\left( {i - k} \right)} \cdot {{\overset{\_}{V}}^{H}\left( {i - k} \right)}}}}},{and}} & \left( {{Equation}\quad 9a} \right) \\{R_{VU} = {\frac{1}{L} \cdot {\sum\limits_{k = 0}^{L - 1}{{\overset{\_}{V}\left( {i - k} \right)} \cdot {{u^{*}\left( {i - k} \right)}.}}}}} & \left( {{Equation}\quad 9b} \right)\end{matrix}$

The empirically calculated FIR MMSE filter is then given by:{overscore (C)}=R _(VV) ⁻¹ ·{overscore (R)} _(VU).  (Equation 9c)While certain features of the invention have been illustrated anddescribed herein, many modifications, substitutions, changes, andequivalents will now occur to those of ordinary skill in the art. It is,therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the spirit ofthe invention.

1. A method comprising: building a linear model of an analogfractional-N phase locked loop unit having a voltage controlledoscillator; and determining a transfer function of a filter that isoptimized according to predefined optimization criteria, wherein saidoptimization criteria are related to an input to said filter and arerelated to an input to said voltage controlled oscillator.
 2. The methodof claim 1, further comprising: including in said model impairments ofone or more components of said phase locked loop unit.
 3. The method ofclaim 1, further comprising: including phase noise in said model.
 4. Themethod of claim 1, further comprising: including in said modelvariations of parameters of said phrase locked loop unit from nominalvalues.
 5. The method of claim 1, wherein determining said transferfunction includes determining said transfer function to be optimizedaccording to said predefined optimization criteria that includes a meansquared error of an input to said filter and an input to said voltagecontrolled oscillator.
 6. The method of claim 1, wherein determiningsaid transfer function includes determining said transfer function to beoptimized according to said predefined optimization criteria thatincludes spectral cleanliness of an output of said voltage controlledoscillator.
 7. The method of claim 1, further comprising: selecting atopology for said transfer function.
 8. The method of claim 1, whereindetermining said transfer function includes determining a finite impulseresponse transfer function.
 9. The method of claim 1, whereindetermining said transfer function includes determining an infiniteimpulse response transfer function.
 10. A method comprising: adjustingdigital values of a filter to compensate for variations in an analogfractional-N phase locked loop unit.
 11. The method of claim 10, whereinadjusting said digital values includes adjusting said digital values tocompensate at least for variations in voltage, temperature, aging, orany combination thereof.
 12. The method of claim 10, wherein adjustingsaid digital values includes adjusting said digital values to compensateat least for variations of parameters of said phase locked loop unitfrom nominal values.
 13. The method of claim 10, further comprising:determining adjusted digital values so that a transfer function of saidfilter is optimized according to predefined optimization criteria.
 14. Afractional-N sigma-delta modulator comprising: a filter having a finiteimpulse response transfer function, said filter coupled to an input of asigma-delta converter; and a fractional-N phase locked loop unit coupledto an output of said sigma-delta converter.
 15. The fractional-Nsigma-delta modulator of claim 14, wherein said transfer function issubstantially equivalent to a transfer function of a minimum meansquared error equalizer.
 16. The fractional-N sigma-delta modulator ofclaim 14, wherein digital values of said filter are to be adjusted sothat said transfer function is optimized according to predefinedoptimization criteria.
 17. The fractional-N sigma-delta modulator ofclaim 16, wherein said optimization criteria includes a mean squarederror of an input to said filter and an input to a voltage controlledoscillator of said fractional-N phase locked loop unit.
 18. Thefractional-N sigma-delta modulator of claim 16, wherein saidoptimization criteria includes spectral cleanliness of an output of avoltage controlled oscillator of said fractional-N phase locked loopunit.
 19. A fractional-N sigma-delta modulator comprising: a sigma-deltaconverter; a fractional-N phase locked loop unit coupled to an output ofsaid sigma-delta converter and including a voltage controlledoscillator; and a filter having an infinite impulse response transferfunction, said filter coupled to an input of said sigma-delta converter,wherein said infinite impulse response transfer function is not aninverse of a transfer function from an output of said filter to an inputof said voltage controlled oscillator.
 20. The fractional-N sigma-deltamodulator of claim 19, wherein digital values of said filter are to beadjusted so that said infinite impulse response transfer function isoptimized according to predefined optimization criteria.
 21. Thefractional-N sigma-delta modulator of claim 20, wherein saidoptimization criteria are related to an input to said filter and arerelated to an input to said voltage controlled oscillator
 22. Thefractional-N sigma-delta modulator of claim 20, wherein saidoptimization criteria includes spectral cleanliness of an output of saidvoltage controlled oscillator.
 23. A fractional-N sigma-delta modulatorcomprising: an adaptive filter coupled to an input of a sigma-deltaconverter; and a fractional-N phase locked loop unit coupled to anoutput of said sigma-delta converter.
 24. The modulator of claim 23,wherein a transfer function of said adaptive filter is a finite impulseresponse.
 25. The modulator of claim 23, wherein said fractional-N phaselocked loop unit includes a voltage controlled oscillator, and wherein atransfer function of said adaptive filter is not an inverse of atransfer function from an output of said filter to an input of saidvoltage controlled oscillator.
 26. A communication device comprising: adipole antenna; a power amplifier coupled to said dipole antenna; and afractional-N sigma-delta modulator coupled to said power amplifier, saidfractional-N sigma-delta modulator including at least: a filter coupledto an input of a sigma-delta converter; and a fractional-N phase lockedloop unit coupled to an output of said sigma-delta converter, wherein atransfer function of said filter is to be optimized according topredefined optimization criteria.
 27. The communication device of claim26, wherein said transfer function is a finite impulse response.
 28. Thecommunication device of claim 26, wherein said transfer function is aninfinite impulse response.
 29. A communication system comprising: afirst communication device; and a second communication device includingat least: a fractional-N sigma-delta modulator including at least: afilter coupled to an input of a sigma-delta converter; and afractional-N phase locked loop unit coupled to an output of saidsigma-delta converter, wherein a transfer function of said filter is tobe optimized according to predefined optimization criteria.
 30. Thecommunication system of claim 29, wherein said transfer function is afinite impulse response.
 31. The communication system of claim 29,wherein said transfer function is an infinite impulse response.